Industry trends aimed at integrating higher levels of circuit functionality have triggered a proliferation of mixed analog-digital systems. Magnified noise coupling through the common chip substrate has made the design and verification of such systems an increasingly difficult task. In this paper we present a fast eigendecomposition technique that accelerates operator application in BEM methods and avoids the dense-matrix storage while taking all of the substrate boundary effects into account explicitly. This technique can be used for accurate and efficient modeling of substrate coupling effects in mixed-signal integrated circuits.